As the proceedings were going on on the first day of a two-day special session, the two, sitting in the Visitors' Gallery, threw papers in the House and jeered at Health Minister Satyendar Jain.
They raised slogans of 'Inquilab Zindabad' and demanded Jain resign.
The two, identified as Jagdeep Rana, who had contested the 2013 Assembly elections from Adarsh Nagar, and Rajan Kumar, were whisked away immediately.
Tyagi and AAP MLA Amantullah Khan allegedly thrashed the duo outside the House.
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Former minister and rebel AAP leader Kapil Mishra said they would have "killed" the accused if police were not called in.
Afterwords, AAP MLA Saurabh Bharadwaj moved a motion against them, which was adopted unanimously, and Speaker Ram Niwas Goel sentenced the two to one month of "rigorous" imprisonment.
The Speaker also wrote to the Tihar Jail Superintendent to keep the duo in custody for the period of one month.
A highly placed source said Rana and Kumar - "disgruntled AAP volunteer" - reportedly got entry on passes with a reference of an AAP MLA. They came wearing headgear.
BJP MLA Manjinder Singh Sirsa demanded strict punishment against those responsbile for arranging their entry.
However, Speaker said they were not allowed in because of reference of any MLA but were let in by House staff.
Chief Minister Arvind Kejriwal was not in the House when the incident took place.
In pamphlets, the duo have claimed they were AAP workers and were unhappy with the Kejriwal-led party and the "corruption cases" against Jain.
The Speaker also ordered that before any MLA recommends passes for anybody wishing to enter the Assembly, he or she has to verify their antecedents and give it in writing.
AAP sources said Rana had recently "aligned" himself with rebel AAP MLA Kapil Mishra.